1. Affine Geometry 1.1. Affine Space 1.2. Affine Lines 1.3. Affine transformations 1.4. Affine Collinearity 1.5. Conic Sections 2. Projective Geometry 2.1. Perspective 2.2. Projective Plane 2.3. Projective Transformations 2.4. Projective Collinearity 2.5. Conics 3. Geometries and Groups 3.1. Transformation Groups 3.2. Erlangen Program 4. Non-Euclidean Geometry 4.1. Elliptic Geometry 4.2. Hyperb...

It is shown that the generalized geometries may be obtained as a deformation of the proper Euclidean geometry. Algorithm of construction of any proposition S of the proper Euclidean geometry E may be described in terms of the Euclidean world function σE in the form S (σE). Replacing the Euclidean world function σE by the world function σ of the geometry G, one obtains the corresponding proposit...

In this paper, an interesting symmetry in Euclidean geometry, which is broken Lorentz studied. As it turns out, attempting to minimize the integral of square scalar curvature leads completely different results these two cases. The main concern paper about metrics R3, are close being invariant under rotation. If we add a time-axis and let metric start rotate with time, out that, case (locally) (...